FE Environmental Fundamental Principles Practice Problems

The current FE Environmental specification assigns 7-11 of the 110 exam questions to Fundamental Principles. Form A contains 8 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

An aerated lagoon is modeled as a completely mixed flow reactor at steady state. The lagoon receives 2,400 m $^{3}$ /d with a soluble BOD of 180 mg/L, its liquid volume is 9,600 m $^{3}$ , and soluble BOD is removed by a first-order reaction with $k = 0.35$ d $^{- 1}$ . The effluent soluble BOD is most nearly:

(A)75 mg/L
(B)105 mg/L
(C)129 mg/L
(D)166 mg/L

Show worked solution

Answer: (A)

Complete mixing forces the entire reactor to sit at its effluent concentration, and the steady-state balance then fixes that concentration at 75 mg/L.

Hydraulic residence time follows from the liquid volume and the throughput flow.

τ = \frac{V}{Q} = \frac{9 , 600}{2 , 400} = 4.0 d

A steady-state balance sets the influent load equal to the effluent load plus the reaction loss, and because the tank contents are at the effluent concentration the reaction term uses $C$ rather than $C_{0}$ .

Q C_{0} = QC + k C V

C = \frac{C _{0}}{1 + k τ} = \frac{180}{1 + ( 0.35 ) ( 4.0 )} = 75 mg/L

FE Reference Handbook — Environmental Engineering: Completely Mixed Flow Reactor, First-Order Reaction

Why the other choices appear

(B)Reports the BOD removed, 180 - 75 = 105 mg/L, instead of the concentration leaving the lagoon.
(C)Omits the unity term in the denominator, 180/[(0.35)(4.0)] = 129 mg/L.
(D)Inverts the residence time to Q/V = 0.25 d, giving 180/[1 + (0.35)(0.25)] = 166 mg/L.